Uncertainty Quantification for Multimodal Large Language Models with Incoherence-adjusted Semantic Volume

Gregory Kang Ruey Lau; Hieu Dao; Nicole Kan Hui Lin; Bryan Kian Hsiang Low

cs.AIFeb 27, 2026

Uncertainty Quantification for Multimodal Large Language Models with Incoherence-adjusted Semantic Volume

Authors: Gregory Kang Ruey Lau, Hieu Dao, Nicole Kan Hui Lin, Bryan Kian Hsiang Low

Organizations: Department of Computer Science, National University of Singapore

Abstract

Despite their capabilities, Multimodal Large Language Models (MLLMs) may produce plausible but erroneous outputs, hindering reliable deployment. Accurate uncertainty metrics could enable escalation of unreliable queries to human experts or larger models for improved performance. However, existing uncertainty metrics have practical constraints, such as being designed only for specific modalities, reliant on external tools, or computationally expensive. We introduce UMPIRE, a training-free uncertainty quantification framework for MLLMs that works efficiently across various input and output modalities without external tools, relying only on the models' own internal modality features. UMPIRE computes the incoherence-adjusted semantic volume of sampled MLLM responses for a given task instance, effectively capturing both the global semantic diversity of samples and the local incoherence of responses based on internal model confidence. We propose uncertainty desiderata for MLLMs and provide theoretical analysis motivating UMPIRE's design. Extensive experiments show that UMPIRE consistently outperforms baseline metrics in error detection and uncertainty calibration across image, audio, and video-text benchmarks, including adversarial and out-of-distribution settings. We also demonstrate UMPIRE's generalization to non-text output tasks, including image and audio generation.

Figures & tables

Figure 1: Schematic describing the UMPIRE framework.

Dataset

AUROC

\uparrow

CPC

\uparrow

ECE

\downarrow

LN-Ent

Sem.Ent

Eigen

Ours

LN-Ent

Sem.Ent

Eigen

Ours

LN-Ent

Sem.Ent

Eigen

Ours

[I] VQAv2

76.5 ±0.1

78.6 ±0.1

84.7 ±0.3

86.7 ±0.2

88.1 ±0.2

78.4 ±1.3

62.6 ±8.9

84.9 ±5.0

93.9 ±0.6

94.6 ±0.1

.343 ±.009

.049 ±.017

.045 ±.002

.048 ±.009

.038 ±.004

[I] OKVQA

53.9 ±0.9

70.3 ±0.1

71.6 ±0.1

73.7 ±0.1

75.3 ±0.1

31.9 ±40.3

71.9 ±12.0

28.8 ±1.8

85.2 ±8.9

96.7 ±0.7

.484 ±.017

.039 ±.002

.194 ±.042

.152 ±.010

.045 ±.007

[I] AdVQA

65.7 ±0.6

64.8 ±0.2

76.4 ±0.2

77.5 ±0.3

78.7 ±0.2

62.4 ±9.5

87.0 ±4.5

75.5 ±0.1

89.2 ±1.3

98.0 ±0.1

.335 ±.012

.077 ±.006

.156 ±.015

.216 ±.005

.039 ±.003

[I] MathVista

75.6 ±0.2

66.9 ±0.3

81.0 ±0.7

81.8 ±0.6

82.6 ±0.6

61.5 ±7.9

82.6 ±2.0

76.7 ±2.4

69.5 ±2.8

83.9 ±2.7

.087 ±.011

.125 ±.018

.189 ±.051

.314 ±.016

.089 ±.015

[I] VQA-RAD

69.7 ±1.3

62.9 ±1.1

76.8 ±0.4

79.5 ±0.6

80.7 ±0.3

47.6 ±4.9

87.1 ±3.4

63.8 ±1.2

62.9 ±4.2

80.8 ±7.1

.139 ±.003

.100 ±.012

.376 ±.019

.352 ±.025

.072 ±.009

Table 1: Effectiveness of various uncertainty metrics across multimodal datasets (details in Section C.1 ). The evaluation covers (i) AUROC (

\times 100

) (

\uparrow

better) ( R1 ), (ii) CPC (

\times 100

) (

\uparrow

better) ( R2R2a ), and (iii) ECE (

\downarrow

better) ( R2R2b ). [I] , [A] , [V] denotes image, audio, video modalities, respectively. Overall, UMPIRE achieves the best or second-best performance across all baselines and modalities, with only marginal gaps when not ranked first. Table 8 in Sec. C.5 provides supplementary results showing that UMPIRE’s performance gains over baselines are statistically significant.

	PUNC	LN-Ent	Eigen	Ours
[I] AnyGPT	44.0 ±2.8	16.6 ±9.8	33.0 ±1.6	81.5 ±3.4
[I] NExTGPT	45.3 ±2.9	36.5 ±12.7	61.6 ±1.7	69.2 ±9.7
[A] NExTGPT	-	74.1 ±14.2	50.4 ±40.9	75.9 ±7.5

Table 2: Pearson Correlation between uncertainty metrics and CLIP/CLAP score for image [I] and audio [A] generation tasks. UMPIRE consistently achieves the highest correlation.

Figure 2: Multimodal coherence R4 : Decrease in AUROC, and ECE when image-input information is (1) corrupted with noise, (2) replaced with a black image, or (3) removed.

Dataset	NC	LN-Ent	Sem.Ent	Eigen	Ours
[I] VQAv2	94.2 ±0.3	95.6 ±0.2	95.4 ±0.1	96.8 ±0.1	97.0 ±0.1
[I] OKVQA	70.6 ±0.6	81.2 ±0.3	79.7 ±0.3	82.5 ±0.2	83.0 ±0.2
[I] AdVQA	73.1 ±0.4	76.1 ±0.7	79.2 ±0.4	80.8 ±0.4	81.4 ±0.5
[I] MathVista	35.0 ±0.2	31.2 ±0.1	38.5 ±0.6	39.4 ±0.1	39.8 ±0.1
[I] VQA-RAD	49.3 ±2.3	52.4 ±0.3	54.7 ±0.9	58.6 ±1.1	60.2 ±0.8
Avg. [I]	64.4 ±0.8	67.3 ±0.3	69.5 ±0.5	71.6 ±0.4	72.3 ±0.4

Table 3: Comparison of AURAC across datasets for different uncertainty metrics, including baselines and UMPIRE.

Figure 3: Performance of uncertainty metrics in blackbox settings across image-text QA datasets. Sem.Ent (D) indicates its discrete version, (Llava) indicates Llava as the white-box proxy model.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Efficiency analysis of UMPIRE compared to baselines. (a) Computational overhead (inference latency in seconds) versus uncertainty estimation performance (AUROC). UMPIRE (red star) achieves state-of-the-art performance with negligible overhead, avoiding the high computational cost associated with semantic equivalence checks in methods like Sem.Ent. (b) The effect of the number of generated responses $k$ on performance. UMPIRE consistently outperforms other methods across all sample sizes and converges to high accuracy even with few generations (e.g., $k=5$ ), demonstrating superior sample efficiency.

Dataset	LR Statistic ( $\chi^{2}$ )	p -value	Significance?
VQAv2	165.30	$<0.0001$	yes
OKVQA	41.49	$<0.0001$	yes
AdVQA	526.33	$<0.0001$	yes
VQA-RAD	30.57	$<0.0001$	yes
MathVista	32.22	$<0.0001$	yes

Appendix

Table 4: Likelihood Ratio Test (LRT) Results. Comparison of model fit between using Incoherence (

Q

) alone versus the Full Model (

Q+U

). Significance (yes/no) denotes

p<0.001

Dataset

AUROC

\uparrow

CPC

\uparrow

ECE

\downarrow

U

Q

V_{\text{adap.}}

V_{\text{best}}

U

Q

V_{\text{adap.}}

V_{\text{best}}

U

Q

V_{\text{adap.}}

V_{\text{best}}

Image-Text

VQAv2

86.7 ±0.2

88.2 ±0.2

88.1 ±0.2

88.0 ±0.1

95.4 ±0.6

88.0 ±0.5

94.6 ±0.1

97.5 ±1.5

.051 ±.007

.070 ±.005

.038 ±.004

.028 ±.011

OKVQA

73.7 ±0.1

75.6 ±0.1

75.3 ±0.1

75.2 ±0.1

85.1 ±8.6

92.4 ±0.4

96.7 ±0.7

93.5 ±6.5

.163 ±.011

.127 ±.002

.045 ±.007

.041 ±.002

AdVQA

77.5 ±0.3

78.7 ±0.2

78.7 ±0.3

89.9 ±1.6

92.4 ±0.4

98.0 ±0.1

97.7 ±0.7

.218 ±.004

.083 ±.003

.039 ±.003

.034 ±.005

MathVista

82.1 ±0.7

83.1 ±0.6

82.6 ±0.6

82.8 ±0.5

71.4 ±1.3

79.1 ±5.2

83.9 ±2.7

85.7 ±4.9

.308 ±.013

.029 ±.006

.089 ±.015

.083 ±.035

Appendix

Table 5: We compare the unadjusted semantic volume

U

, Monte Carlo estimate of the expected incoherence value or quadratic entropy

Q

, and our final form of UMPIRE

V

. We report two values for

V

V_{adap}

which uses

\alpha

based on the adaptive

\alpha

heuristic that does not require labeled data, and

V_{best}

which uses

\alpha

found based on a held-out labeled development set.

Subset Size	AUROC	ECE	CPC	AURAC
1%	0.882	0.04	0.948	0.966
5%	0.882	0.038	0.947	0.966
10%	0.882	0.038	0.946	0.966

Appendix

Table 6: UMPIRE performance is robust to the size of unlabeled set of task instance that we use to compute adaptive

\alpha

. Results are computed on VQAv2 validation set.

Metric	Method	Image					Audio		Video	Avg
Metric	Method	VQAv2	OKVQA	AdVQA	MathVista	VQA-RAD	SLUE-P2 SQA5	Spoken SQuAD	Video-MME short	Avg
TPR@10% FPR $\uparrow$	NC	0.362	0.095	0.189	0.408	0.189	-	-	-	0.249
	LN-Ent	0.282	0.244	0.168	0.347	0.127	0.299	0.248	0.287	0.250
	Sem.Ent	0.574	0.327	0.419	0.437	0.511	0.557	0.464	0.311	0.450
	Eigen	0.602	0.340	0.466	0.483	0.601	0.443	0.435	0.534	0.488
	Ours	0.629	0.369	0.477	0.497	0.587	0.522	0.490	0.539	0.514

Appendix

Table 7: True Positive Rates (TPR) at different False Positive Rate (FPR) thresholds for various uncertainty quantification methods across multimodal tasks. Results are reported at FPR levels of 10% and 1%.

Figure 6: Pearson correlation plots of the uncertainty scores $u$ on the VQAv2, OKVQA, and AdVQA, which demonstrate UMPIRE’s strong correlation compared to other metrics.

	LN-Ent	EigenScore	SE
AUROC ( R1 )
t-test p-value	$1.03\times 10^{-5}$	$2.25\times 10^{-8}$	$1.94\times 10^{-6}$
wilcoxon test p-value	$1.95\times 10^{-3}$	$1.95\times 10^{-3}$	$1.95\times 10^{-3}$
CPC ( R2R2a )
t-test p-value	$4.50\times 10^{-4}$	$9.15\times 10^{-4}$	$1.06\times 10^{-2}$
wilcoxon test p-value	$1.95\times 10^{-3}$	$1.95\times 10^{-3}$	$1.95\times 10^{-3}$

Appendix

Table 8: Statistical tests calculated based on the results from models: Llava-13B, Llava-7B and Mllama-11B with datasets: VQAv2, AdVQA and OKVQA. The p-value of both tests are

\ll

0.01, thus there is sufficient evidence at the 1% level of significance to conclude that

X_{UMPIRE}-X_{other}>0

for the metrics AURAC, CPC, AUROC, and

X_{UMPIRE}-X_{other}<0

for ECE.

Figure 7: Qualitative example of $U$ correcting model overconfidence. The model incorrectly predicts ”Parking” with high confidence, causing the Incoherence score ( $Q$ ) to fail (predicting ”Certain”). However, because the sampled responses (”Traffic”, ”Dump”, ”Truck”) are semantically scattered, the high semantic volume ( $U$ ) correctly identifies the confusion, allowing UMPIRE to successfully detect the error.

Figure 8: Qualitative example of UMPIRE’s robustness on tasks with low semantic variance (e.g., yes/no, counting). While the clustered embeddings of the sampled answers (digits) fool $U$ into predicting certainty, UMPIRE uses the high Incoherence score ( $Q$ ) to correctly flag the prediction as uncertain.

Dataset	Method	AUROC $\uparrow$	ECE $\downarrow$	CPC $\uparrow$
VQAv2	Seq Prob	0.632	0.121	0.374
	Mean Token Entropy	0.628	0.129	0.046
	Perplexity	0.629	0.131	0.125
	Ours (k=5)	0.873	0.067	0.923
ADVQA	Seq Prob	0.595	0.303	0.372
	Mean Token Entropy	0.590	0.302	0.170

Appendix

Table 9: Comparison of the performance of single sampling methods and UMPIRE across various VQA datasets.

Figure 9: Ablation study on choosing the layer index to extract embedding vectors. Results show that different layer indices only have slight variations in the AUROC performance.

Figure 10: Ablation study on the (a) Impact of temperature during the generation process on evaluation performance. (b) Evaluation methods. UMPIRE consistently outperforms baseline approaches regardless of the chosen evaluation functions.

Figure 11: Results for the effect of number of bins on (a) CPC and (b) ECE. Both measures show that UMPIRE consistently outperforms baselines.

Figure 12: Ablation study across different models on image-text (VQAv2) and audio-text (SLUE-P2-SQA5) understanding datasets, evaluating AUROC performance for LN-Ent, Sem.Ent, Eigen, and UMPIRE. The results indicate that UMPIRE consistently achieves strong AUROC across various models, including Llava-v1.5-7b, Llava-v1.5-13b, Llama-3.2-11B-Vision, Llama-3.2-90B-Vision , cogvlm2-llama3-chat-19B , Qwen2.5-VL-7B-Instruct for image-text, and Qwen2-Audio-7B , Phi4 for audio-text. This highlights the robustness and effectiveness of our approach across different model architectures.

Figure 13: UMPIRE metric consistently outperforms other baselines across various black-box models, including GPT4o, GPT4o-mini, and Claude 3.5 Haiku.

Method	AUROC $\uparrow$	CPC $\uparrow$	ECE $\downarrow$
UMPIRE ( Llava-v1.5-13b )	0.890	0.904	0.094
UMPIRE ( Llava-v1.5-7b )	0.893	0.900	0.087
UMPIRE ( Llama-3.2-11B-Vision )	0.839	0.943	0.091

Appendix

Table 10: Results of UMPIRE in blackbox settings with different proxy models.

Metric	Method	VQAv2	AdVQA	OKVQA	MathVista	VQA-Rad
AUROC ↑	Without Length Normalized	0.882	0.787	0.755	0.822	0.802
AUROC ↑	Length Normalized	0.875	0.779	0.756	0.825	0.792
CPC ↑	Without Length Normalized	0.946	0.979	0.966	0.945	0.908
CPC ↑	Length Normalized	0.986	0.978	0.946	0.936	0.935
ECE ↓	Without Length Normalized	0.038	0.042	0.036	0.071	0.067
ECE ↓	Length Normalized	0.062	0.019	0.034	0.056	0.068

Appendix

Table 11: Comparison of UMPIRE with and without length normalization across various VQA datasets.

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Multimodal Large Language Models (MLLMs) are increasingly deployed in safety-critical settings, yet estimating when their answers can be trusted remains underexplored. We systematically compare training-free verbalized, token-level and semantic uncertainty estimation methods on twelve MLLMs and five VQA benchmarks. We find that answer length decides which family wins: token-level entropy on short answers, verbalized methods on sentence-length responses, and semantic methods on long-form generation. Token-level entropy becomes far more informative when estimated at a higher temperature than the low ones used to generate answers, and asking a model to judge its own answer becomes more reliable with model size. Building on this, a length-aware recipe that additionally flags responses on which the model abstains outperforms every individual method on average at about a quarter of the cost of semantic methods, although no method attains the coverage required for safe deployment. These results provide practitioners with principled guidance for selecting estimators by answer length and model scale.

Abstract

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